One side of an object appears normal but the other side is transparent
2.49b:

Try adding some thickness to your mesh. 

It seems to be currently a 2 dimensional plane, which will only have one side drawn unless double sided faces is enabled.

2.6x:

It seems that double sided faces was removed in 2.6x.
Backface culling can also cause this.
The Backface culling setting is located in 3D view > Properties panel > Display: